 
Summary: Homework 6
1. Problem 1 page 249. In class, we used to represent a fixed amount that was lost in every iteration.
For this problem, assume is percent of remaining that the player gets to keep. Thus, is a percent
retained rather than a fixed amount.
2. Suppose we have two stage bargaining. Suppose there are different discount factors for each player.
In other words, I might lose a different amount from a strike than the firm does. (I lose a month's
wages. The firms loses public good will.) Both discounts are publicly known. In two stage
bargaining, how is player 1's share affected as his/her discount gets closer and closer to 100%,
assuming that player 1's discount doesn't change?
3. Define: The core of a coalition game with transferable payoff is the set of feasible payoff
profiles for all members of the group for which there is no subcoalition and payoff vector for
which everyone does better.
Suppose that three players can obtain one unit of payoff together and any two of them can share
between them. Under what circumstances is the core nonempty?
4. Amy has 16 bananas and no apples. Betty has 16 apples and no bananas. Let x1 be the number of
bananas a person has. Let x2 be the number of apples a person has. Let Amy's utility function be
(x1+x2). Let Betty's utility be min(x1,x2). Draw the edgewood box showing the disagreement point,
the indifference curves, the lens of trade, and the pareto optimal trades.
5. Player i is a dummy if v(S{i}) v(S) = v({i}). What should player i's payoff be in any stable
allocation?
